We showed in this article that numerous concepts from different fields of
mathematics and computer science are closely related, non-positively curved
spaces and rewriting systems with the cube property in particular, 
These are important observations since, in many ways, non-positively curved
spaces are “simpler” to work with than general spaces: topological invariants
are much simpler, the homology and homotopy groups have no torsion, and
their universal covering space are contractible [1]}.
